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Sum of the products of the digits of n and the positions of the digits m in n starting from the last digit.
3

%I #7 Dec 02 2018 15:04:11

%S 1,2,3,4,5,6,7,8,9,2,3,4,5,6,7,8,9,10,11,4,5,6,7,8,9,10,11,12,13,6,7,

%T 8,9,10,11,12,13,14,15,8,9,10,11,12,13,14,15,16,17,10,11,12,13,14,15,

%U 16,17,18,19,12,13,14,15,16,17,18,19,20,21,14,15,16,17,18,19,20,21,22,23,16,17,18,19,20,21,22,23,24,25,18,19,20,21,22,23,24,25,26,27,3

%N Sum of the products of the digits of n and the positions of the digits m in n starting from the last digit.

%C Starts to differ from A081594 when n>=100. [From _R. J. Mathar_, Feb 19 2009]

%F Let n = d(1)d(2)...d(m) where d(1),d(2),...,d(m) are the digits of n. Then a(n) = m*d1+(m-1)*d2+...+d(m).

%e a(19) = 9*1 + 1*2 = 11.

%p A156230 := proc(n)

%p local dgs;

%p dgs := convert(n,base,10) ;

%p add(i*op(i,dgs),i=1..nops(dgs)) ;

%p end proc:

%p seq(A156230(n),n=1..100) ; # _R. J. Mathar_, Dec 02 2018

%t pdn[n_]:=Module[{idn=IntegerDigits[n]},Total[idn Range[Length[idn],1,-1]]]; Array[pdn,80] (* _Harvey P. Dale_, Aug 22 2012 *)

%o (PARI) gr(n) = v=Vec((rev(n)));sum(x=1,length(v),x*eval(v[x]))

%o gr1(n) = for(j=1,n,print1(gr(j)","))

%o rev(str) = /* Get the reverse of the input string

%o */ {

%o local(tmp,s,j);

%o tmp = Vec(Str(str));

%o s="";

%o forstep(j=length(tmp),1,-1,

%o s=concat(s,tmp[j]));

%o return(s)

%o }

%K base,nonn

%O 1,2

%A _Cino Hilliard_, Feb 06 2009

%E Changed the description, formula and Pari code _Cino Hilliard_, Feb 08 2009

%E More terms to separate from A322001. - _R. J. Mathar_, Dec 02 2018